# How do you solve using the quadratic formula for y = 12x^2 - 35x + 8?

May 16, 2015

$y = 12 {x}^{2} - 35 x + 8 = 0$

$D = {d}^{2} = {b}^{2} - 4 a c = 1225 - 384 = 841 \to d = \pm 29$

$x = \frac{35}{24} + \frac{29}{24} = \frac{64}{24} = \frac{8}{3}$

$x = \frac{35}{24} - \frac{29}{24} = \frac{6}{24} = \frac{1}{4}$

There is another way: solving by the new Transforming Method (Google , Yahoo Search) that may be faster and not boring, especially when you can't use calculator.
$y = 12 {x}^{2} - 35 x + 8$
Transformed equation : $y ' = {x}^{2} - 35 x + 96 \left(a . c = 12 \left(8\right) = 96\right)$
Solve y' by composing factor pairs of (96). Proceed: (2, 48)(3, 32).
This last sum is 35 = -b. Then its 2 real roots are: p' = 3 and q' = 32. Back to original equation, the 2 real roots are: $p = \frac{p '}{a} = \frac{3}{12} = \frac{1}{4} , \mathmr{and} q = \frac{q '}{a} = \frac{32}{12} = \frac{8}{3.}$